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Special Topic I
117
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Fraction Present in the Acidic or the Basic Form
A common question asked is what fraction of a buffer will be in a particular form at a given pH—either what
fraction will be in the acidic form or what fraction will be in the basic form.
This is an easy question to answer if you remember the following formulas that are derived at the end of this section:
fraction present in the acidic form
=
[ ]
[ ]
H
H
a
+
+
+
K
fraction present in the basic form
=
K
K
a
a
H
+
+
[ ]
What fraction of an acetic acid/sodium acetate buffer
1
p
K
a
of acetic acid
=
4.76;
K
a
=
1.74
*
10
-
5
2
is present in
the acidic form at
pH
=
5.20;
3
H
+
4
=
6.31
*
10
-
6
?
[ ]
[ ]
) (
)
H
H
6.31 10
(1.74 10
6.31 10
6.31 10
(17.
a
6
5
6
6
+
+
−
−
−
−
+
=
×
×
+
×
=
×
K
4 10
6.31 10
6.31 10
23.7 10
6.31
23.7
0.26
6
6
6
6
×
+
×
= ×
×
=
=
−
−
−
−
) (
)
What fraction of a formic acid/sodium formate buffer
1
p
K
a
of formic acid
=
3.75;
K
a
=
1.78
*
10
-
4
2
is present
in the basic form at
pH
=
3.90;
3
H
+
4
=
1.26
*
10
-
4
?
K
K
a
a
H
+
=
×
×
+
×
=
×
×
+
−
−
−
−
[ ]
(
) (
)
1 78 10
1 78 10
1 26 10
1 78 10
3 04 1
4
4
4
4
.
.
.
.
.
0
1 78
3 04
0 586
0 59
4
−
=
=
=
.
.
.
.
The formulas describing the fraction present in the acidic or basic form are obtained from the definition of the acid
dissociation constant.
K
a
H A
HA
=
[ ]
+ −
[ ] [ ]
To derive the equation for the fraction present in the acidic form, we need to define
3
A
-
4
in terms of [HA], so we
have only one unknown in the equation.
[ ]
[ ]
A
HA
H
a
−
+
=
[ ]
K